Proportionally fair - Revision history

137.226.12.27 at 10:42, 25 August 2014

2014-08-25T10:42:46Z

← Older revision		Revision as of 12:42, 25 August 2014
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	~~In [[mathematics]]~~ and ~~[[statistics]], an '''asymptotic distribution''' is a hypothetical distribution that is in a sense~~ the ~~"limiting" distribution of~~ a ~~sequence of distributions~~. ~~One of the main uses of the idea~~ of ~~an asymptotic distribution~~ is ~~in providing approximations to the [[cumulative distribution function]]s of statistical [[estimator]]s.~~		Myrtle Benny is how I'm known as and I feel comfy when people use the complete title. I am a meter reader. He is truly fond of doing ceramics but he is struggling to find time for it. South Dakota is where me and my husband reside.<br><br>Feel free to surf to my web page ... [http://exchange.craftemergency.org/thankyous/can-men-be-sexually-harassed-ladies exchange.craftemergency.org]

	~~==Definition==~~

	~~A sequence of distributions corresponds~~ to ~~a sequence of random variables Z<sub>i</sub>~~ for ~~''i'' = 1, 2,~~ ... . In the simplest case, an asymptotic distribution exists if the probability distribution of Z<sub>i</sub> converges to a probability distribution (the asymptotic distribution) as ''i'' increases: see [[Convergence of random variables#Convergence in distribution\|convergence in distribution]]. A special case of an asymptotic distribution is when the sequence of random variables always approaches zero—that is, the Z<~~sub~~>i<~~/sub~~> go to ~~0 as i goes~~ to ~~infinity~~. ~~Here the asymptotic distribution is a [[degenerate distribution]], corresponding to the value zero~~.

	~~However, the most usual sense in which the term asymptotic distribution is used arises where the random variables Z<sub>i</sub> are modified by two sequences of non-random values~~. ~~Thus if~~
	:~~<math>Y_i=\frac{Z_i-a_i}{b_i}</math>~~
	~~converges in distribution to a non-degenerate distribution for two sequences {''a<sub>i<~~/~~sub>''} and {''b<sub>i<~~/~~sub>''} then Z<sub>i</sub> is said to have that distribution as its asymptotic distribution~~. ~~If the distribution function of the asymptotic distribution is ''F'' then, for large ''n'', the following approximations hold~~
	~~:<math>P\left(\frac{Z_n-a_n}{b_n} \le x \right) \approx F(x) ,<~~/~~math>~~
	~~:<math>P(Z_n \le z) \approx F\left(\frac{z-a_n}{b_n}\right) .<~~/~~math>~~

	If an asymptotic distribution exists, it is not necessarily true that any one outcome of the sequence of random variables is a convergent sequence of numbers. It is the sequence of probability distributions that converges.

	~~==Asymptotic normality==~~
	~~{{seealso\|local asymptotic normality}}~~
	Perhaps the most common distribution to arise as an asymptotic distribution is the [[normal distribution]]. In particular, the [[central limit theorem]] provides an example where the asymptotic distribution is the [[normal distribution]].

	~~Barndorff~~-~~Nielson & Cox<ref>Barndorff~~-~~Nielson, O.E., Cox, D.R. (1989) Asymptotic Techniques for Use in Statistics. Chapman and Hall. ISBN 0~~-~~412~~-~~31400~~-~~2</ref> provide a direct definition of asymptotic normality.~~

	The [[Binomial distribution]] seems to be the first asymptotic approximation by a [[normal distribution]]; compared to the more general case of [[central limit theorem]], convergence of the Binomial to the normal is especially rapid.~~{{cn\|date=March 2011}} Asymptotic normality of the [[Binomial distribution]] is proven by the [[de Moivre–Laplace theorem]]~~.~~{{cn\|date=March 2011}}~~

	~~==See also==~~
	*[[Asymptotic theory]]
	*[[Central limit theorem]]
	*[[de Moivre–Laplace theorem]]
	*[[Limiting density of discrete points]]

	~~==References==~~
	~~{{Reflist}}~~

	~~[[Category:Theory of probability distributions]]~~
	~~[[Category:Asymptotic statistical theory]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-28T21:53:40Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 23:53, 28 January 2014
Line 1:		Line 1:
	~~Hello~~, ~~my title~~ is ~~Andrew and my spouse doesn~~'~~t like it at all~~. ~~To climb~~ is ~~some thing I really enjoy performing~~. ~~Invoicing~~ is ~~my profession~~. ~~Alaska~~ is ~~exactly~~ where I'~~ve always been residing.~~<br><br>~~Feel free~~ to ~~visit my web blog~~: ~~best psychic~~ (~~[http~~://~~gcjcteam~~.~~org/index~~.~~php?mid~~=~~etc_video&document_srl~~=~~696611&sort_index~~=~~regdate&order_type~~=~~desc http~~:~~//gcjcteam.org/~~])		In [[mathematics]] and [[statistics]], an '''asymptotic distribution''' is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the [[cumulative distribution function]]s of statistical [[estimator]]s.

			==Definition==

			A sequence of distributions corresponds to a sequence of random variables Z<sub>i</sub> for ''i'' = 1, 2, ... . In the simplest case, an asymptotic distribution exists if the probability distribution of Z<sub>i</sub> converges to a probability distribution (the asymptotic distribution) as ''i'' increases: see [[Convergence of random variables#Convergence in distribution\|convergence in distribution]]. A special case of an asymptotic distribution is when the sequence of random variables always approaches zero—that is, the Z<sub>i</sub> go to 0 as i goes to infinity. Here the asymptotic distribution is a [[degenerate distribution]], corresponding to the value zero.

			However, the most usual sense in which the term asymptotic distribution is used arises where the random variables Z<sub>i</sub> are modified by two sequences of non-random values. Thus if
			:<math>Y_i=\frac{Z_i-a_i}{b_i}</math>
			converges in distribution to a non-degenerate distribution for two sequences {''a<sub>i</sub>''} and {''b<sub>i</sub>''} then Z<sub>i</sub> is said to have that distribution as its asymptotic distribution. If the distribution function of the asymptotic distribution is ''F'' then, for large ''n'', the following approximations hold
			:<math>P\left(\frac{Z_n-a_n}{b_n} \le x \right) \approx F(x) ,</math>
			:<math>P(Z_n \le z) \approx F\left(\frac{z-a_n}{b_n}\right) .</math>

			If an asymptotic distribution exists, it is not necessarily true that any one outcome of the sequence of random variables is a convergent sequence of numbers. It is the sequence of probability distributions that converges.

			==Asymptotic normality==
			{{seealso\|local asymptotic normality}}
			Perhaps the most common distribution to arise as an asymptotic distribution is the [[normal distribution]]. In particular, the [[central limit theorem]] provides an example where the asymptotic distribution is the [[normal distribution]].

			Barndorff-Nielson & Cox<ref>Barndorff-Nielson, O.E., Cox, D.R. (1989) Asymptotic Techniques for Use in Statistics. Chapman and Hall. ISBN 0-412-31400-2</ref> provide a direct definition of asymptotic normality.

			The [[Binomial distribution]] seems to be the first asymptotic approximation by a [[normal distribution]]; compared to the more general case of [[central limit theorem]], convergence of the Binomial to the normal is especially rapid.{{cn\|date=March 2011}} Asymptotic normality of the [[Binomial distribution]] is proven by the [[de Moivre–Laplace theorem]].{{cn\|date=March 2011}}

			==See also==
			*[[Asymptotic theory]]
			*[[Central limit theorem]]
			*[[de Moivre–Laplace theorem]]
			*[[Limiting density of discrete points]]

			==References==
			{{Reflist}}

			[[Category:Theory of probability distributions]]
			[[Category:Asymptotic statistical theory]]

en>Volker pauli: /* User prioritization */ Corrected the interpretation of a larger time constant in PF scheduling.

2011-09-08T06:23:01Z

User prioritization: Corrected the interpretation of a larger time constant in PF scheduling.

New page

Hello, my title is Andrew and my spouse doesn't like it at all. To climb is some thing I really enjoy performing. Invoicing is my profession. Alaska is exactly where I've always been residing.<br><br>Feel free to visit my web blog: best psychic ([http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc http://gcjcteam.org/])